Question 26309
This is a variation an old story.
By placing 1 penny on the first square, two pennies on the second square, three pennies on the third square, etc, Farmer Brown is creating a geometric sequence in which each term can be represented by: (an) where n = the ordinal number of the term. So, a(1) is the first term, a(2) is the second term, etc.
The nth term of such a sequence is given by:{{{a(n) = a(1)*r^(n-1)}}} where a(1) is the first term and (r) is the common ratio and is found by{{{r = a(n+1)/a(n)}}}.
In this problem, r = 2 and a(1) = 1 (penny)

The 32nd term would be {{{a(32) = 1*2^(32-1)}}} = {{{2^31 = 2147483648}}} and, since this is the number of pennies, this would amount to $21,474,836.48 

 Note: a(1) means... a sub 1